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Let lim(xto0) ([x]^(2))/(x^(2))=m, where...

Let `lim_(xto0) ([x]^(2))/(x^(2))=m,` where `[.]` denotes greatest integer. Then, m equals to

A

`-(1)/(sqrt(2))`

B

`(1)/(sqrt(2))`

C

`sqrt(2)`

D

`-sqrt(2)`

Text Solution

Verified by Experts

The correct Answer is:
B
`([x]^(2))/(x^(2))=[{:(0", ""if "0ltxlt1),((1)/(x^(2))","" if "-1ltxlt0):}impliesl " does not exist"`
`([x]^(2))/(x^(2))=[{:(0", ""if "0ltxlt1),(0","" if "-1ltxlt0):}impliesm" exists and is equal to 0"`
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CENGAGE PUBLICATION-LIMITS-Exercises (Single Correct Answer Type)
  1. lim(xto0) [(sin(sgn(x)))/((sgn(x)))], where [.] denotes the greatest i...

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  2. Let lim(xto0) ([x]^(2))/(x^(2))=m, where [.] denotes greatest integer....

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  3. lim(xto1) [cosec(pix)/(2)]^(1//(1-x)) (where [.] represents the greate...

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  4. The value of the limit lim(xto0) (a^(sqrt(x))-a^(1//sqrt(x)))/(a^(sqrt...

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  5. If lim(xtoa) {(f(x))/(g(x))} exists, then which one of the following c...

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  6. lim(xto-1) (1)/(sqrt(|x|-{-x})) (where {x} denotes the fractional part...

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  7. If x1=3a n dx(n+1)=sqrt(2+xn),ngeq1,t h e n""("lim")(xvecoo)xn is -1 ...

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  8. lim(xto0^(-)) (sum(r=1)^(2n+1)[x^(r)]+(n+1))/(1+[x]+|x|+2x), where nin...

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  9. lim(x->oo)(sin^4x-sin^2x+1)/(cos^4x-cos^2x+1) is equal to (a) 0 ...

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  10. If f(x)=2/(x-3),g(x)=(x-3)/(x+4) , and h(x)=-(2(2x+1))/(x^2+x-12) then...

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  11. The value of lim(x->pi)(1+cos^3x)/(sin^2x) is (a)1/3 (b) 2/3 ...

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  12. The value of lim(xto2) (sqrt(1+sqrt(2+x))-sqrt(3))/(x-2)" is "

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  13. The value of ("lim")(xvec2)(2^x+2^(3-x)-6)/(sqrt(2^(-x))-2^(1-x))i s ...

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  14. lim(x->2)(((x^3-4x)/(x^3-8))^(-1)-((x+sqrt(2x))/(x-2)-(sqrt(2))/(sqrt(...

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  15. If lim(xto-2^(-)) (ae^(1//|x+2|)-1)/(2-e^(1//|x+2|))=lim(xto-2^(+)) si...

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  16. lim(xto1) ((1-x)(1-x^(2))...(1-x^(2n)))/({(1-x)(1-x^(2))...(1-x^(n))}^...

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  17. The value of lim(x->1/(sqrt(2))) ((x-"cos" (sin^(-1)x))/ (1-tan(sin^(-...

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  18. Among (i) lim(xtooo) sec^(-1)((x)/(sinx))" and "(ii) lim(xtooo) sec^(-...

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  19. lim(xtooo) ((x^(3))/(3x^(2)-4)-(x^(2))/(3x+2))" is equal to "

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  20. lim(n->oo)(n(2n+1)^2)/((n+2)(n^2+3n-1)) is equal to (a)0 (b) ...

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